随机子空间法.pdf

摘 要 - I - 结构环境振动模态参数识别随机子空间方法与应用 摘 要 环境激励振动试验，具有无须贵重的激励设备，不打断结构的正常使用，方便省 时等显著的优点，更符合土木工程结构的实际使用特点由于环境振动试验仅测量结 构振动响应的输出数据，模态参数识别是仅基于输出数据的识别，不同于传统的基于 输入和输出的模态分析，成为工程结构系统识别十分活跃的研究课题本文对目前先 进的数据驱动式随机子空间识别（SSI）的理论、算法、系统定阶、实桥应用进行了 深入的探讨完成的主要工作和结论包括： 1. 介绍了数据驱动的随机子空间识别理论和算法， 重点讨论了对投影矩阵加权方 法的不同导致的三种随机子空间识别算法：UPC 法，PC 法和 CVA 法通过 对西宁北川河桥环境振动实测数据的处理，分析了这三种方法的异同点计 算结果表明，三种算法相似，计算结果也很接近，从精度上讲，PC 法会稍 好，但相应的计算时间也长些 2. 利用奇异熵的概念， 提出和建立了用奇异谱分析技术和奇异熵增量的导数来 实现数据驱动随机子空间识别方法系统定阶的方法和过程 用四层框架仿真 算例和简支梁试验数据验证了所提系统定阶方法的可靠性。

3. 详细介绍了江西吉安大桥成桥环境振动试验，用随机子空间识别方法得到了该 桥工作状态全桥桥面竖向、横向、纵向空间振动特性以及拱肋竖向、横向的振 动特性试验结果表明，用环境振动相应数据足以识别出该桥主要阶次的模 态及其模态参数 利用所提出的奇异熵增量谱方法对吉安桥实测数据进行了 系统阶次的确定，结果表明该法定阶稳定，可以避免系统定阶的盲目性 4. 建立了江西吉安大桥的空间有限元模型， 比较分析了有限元模态分析和试验 模态分析的结果有限元计算与实测结果吻合良好，表明所建立的吉安大桥有 限元模型可以很好地预测该桥的动力学特性，可作为该桥各种复杂动力响应 分析、长期健康监测和使用状态评估的基础 关键词：环境振动，模态参数识别，随机子空间识别，桥梁结构 ABSTRACT - II - Stochastic Subspace Identification and Application of Structures under Ambient Vibration Stochastic Subspace Identification and Application of Structures under Ambient Vibration Abstract Dynamic testing of structures under ambient vibration excitation has many advantages, such as no excitation equipment needed, no interruption of structural service conditions and less test time, which is more close to the real working conditions of civil engineering structures. As only output is measured and real input remains unknown in terms of ambient vibration testing, the modal parameter identification therefore bases structural output-only data. The output-only modal parameter identification is different from traditional one and is now very active research topic in the system identification of engineering structures. The state-of-the-art studies are carried out in this thesis on the theory, algorithm, system order determination and real case applications of the data-driven stochastic subspace identification (SSI). The main work and conclusions include: 1. The theoretical background of the data-driven stochastic subspace identification is discussed. The study is focused on three algorithms: Unweighted Principal Component (UPC) Algorithm, Canonical Variate Algorithm (CVA) and Principal Component Algorithm (PC) due to the different treatments on the projected matrix of SSI. The ambient vibration measurements on a real case arch bridge-Beichuan Bridge in Xilin, China, are used to compare the modal parameter identification results obtained from three algorithms. It is demonstrated that these three algorithms are close together. In terms of identification accuracy, the PC algorithm is the best but it is also time consuming. 2. How to determine the system order is so far still a problem among time-domain system identification techniques. Based on the concept of singularity entropy in this thesis, the singularity entropy increment and its derivative are proposed to determine the system order incorporated with the stochastic subspace identification. One 4-strory frame and one simply beam are used to demonstrate the applicability and reliability of proposed singularity entropy based methods. 3. The field ambient vibration tests on the Jian arch bridge in Jiangxi Province is described in details. The stochastic subspace identification has been used ABSTRACT - III - successfully to identify the three-dimensional vibration modes of bridge deck and arch ribs. It is demonstrated that the bridge ambient vibration measurements are enough to identify the dominated vibration modes of such a large-scale bridge. In addition, the proposed singularity entropy based method is implemented to determine the system order of Jian bridge. It is again verified that the proposed singularity entropy based method is stable in the determination of system order. 4. A three-dimensional finite element model of the Jian bridge is established in the thesis. The modal analysis results obtained from finite element calculation have been compared with those identified from the field ambient vibration measurements. A good agreement has been achieved. The calibrated finite element model that reflects the built-up structural dynamic properties can be served as a baseline model in the succeeding dynamic response analysis under complicated excitations, long-term health monitoring and structural condition assessment of the Jian bridge. Key words: Ambient vibration, Modal Parameter Identification, Stochastic Subspace Identification, Bridge 目 录 IV 目 录 第一章 绪论.1 1.1 模态分析和模态参数识别.1 1.2 经典的模态参数识别方法.2 1.3 环境振动模态分析.3 1.4 环境振动模态参数识别回顾.4 1.4.1 峰值拾取法(Peak-picking method) 4 1.4.2 频域分解法 5 1.4.3 联合时频域方法5 1.4.4 时间序列分析法5 1.4.5 随机减量法6 1.4.6 NExT 法.6 1.4.7 随机子空间方法(Stochastic Subspace Identification-SSI)6 1.5 本文的主要工作.7 第二章 随机子空间识别方法.9 2.1 引言 9 2.2 系统的状态空间方程描述.10 2.2.1 连续状态空间方程10 2.2.2 离散状态空间方程11 2.2.3 随机状态空间方程12 2.3 模态参数提取.13 2.4 随机子空间算法.14 2.4.1 Hankel 矩阵的组成14 2.4.2 卡尔曼滤波状态序列15 2.4.3 识别系统矩阵 16 2.5 三种随机子空间方法的应用和比较.18 2.5.1 三种随机子空间方法介绍 .18 2.5.2 三种随机子空间方法的比较.19 2.6 本章小结23 第三章 基于奇异熵的系统定阶方法24 3.1 引言 24 3.2 奇异谱理论 24 目 录 V 3.3 奇异熵 25 3.3.1 信息熵。